Indeed, avoiding the perception of impropriety is second only to avoiding impropriety itself. When people perceive impropriety, even when there is none, trust in the system is undermined.

At the end of the day it's up to everybody to apply their own version of the "reasonable person" test. Might a reasonable person misconstrue what you're doing to be unethical? If so, rethink your approach. Maybe there is no other option, but often there is.

Anything could be perceived as a conflict of interest. This entire subthread is an argument about whether it’s reasonable to consider this case a conflict of interest.